A Tverberg type theorem for matroids

Abstract

Let b(M) denote the maximal number of disjoint bases in a matroid M. It is shown that if M is a matroid of rank d+1, then for any continuous map f from the matroidal complex M into the d-dimensional Euclidean space there exist t \geq \sqrt{b(M)}/4 disjoint independent sets σ_1,\ldots,σ_t \in M such that \bigcap_{i=1}^t f(σ_i) \neq \emptyset.

This article is due to be published in the collection of papers "A Journey through Discrete Mathematics. A Tribute to Jiri Matousek" edited by Martin Loebl, Jaroslav Nesetril and Robin Thomas, due to be published by Springer